In the CDC article from OP, combination filtration and disinfection has a very high effectiveness on everything.
Long ago I was sick from bad water and it wasn't fun. Very keen to avoid that experience again. The water at the time was pumped straight from a dam, no treatment. Long drought, then rains washed all sorts of stuff into the dam. At the time, I naively thought all towns had water treatment. In Australia, small towns may not. I've had to treat "town water". Also, some towns have several different water sources. St George, QLD for example has three: rain water, bore water and water pumped straight from the river. So you really need to check which tap you fill up from. The locals list them as: Drink, wash, water the garden.
I filter first, than use chlorine. The chlorine then stays in my drinking containers – helping keep them clean.
I've read that bacteria in water clump up – either together or to other particles in the water. http://www.who.int/water_sanitation_health/resourcesquality/wqmchap10.pdf
So I figure that filtering first removes these clumps. Removing organic matter improves the chlorine application also; read the instructions about how very dirty water may require more than the standard dosage.
I put a lot of time into researching the likely water bugs, and it seemed to me, that the larger sized bugs which are easy to filter are the ones most resistant to chlorine and iodine. The smaller stuff, harder to filter, dies quicker with chlorine or iodine.
Currently using a Sawyer filter in a gravity system.
Using Katadyn Micropur, which list the treatment times as "Contact Time: 30 min for bacteria and viruses, 2 h for Giardia in clear water." http://www.katadyn.com/en/katadyn-products/products/katadynshopconnect/katadyn-micropur-micropur-forte/micropur-forte-mf-1t-enplczhuru/
Since I've filtered the water – no giardia. So 30 minutes is all I need. I can wait that long.
I use chlorine over iodine as its impossible to poison yourself with too much chlorine. The water smells like a pool, and your not going to drink it. Leave it sit, aerate it, or add a vitamin C tablet to neutralize the chlorine (after the 30 minutes) and your good to go.
If my filter fails, I can "Super Chlorinate". Add excess chlorine, wait, then neutralise. (I carry other chlorine besides the micropur tablets as well. Re-supply in parts of Australia is measured in weeks.) Chlorine can be mixed up for cleaning.
Iodine – has no indicator you have too much in the water. It is more problematic for your health if you have too much. I'd rather not have to worry about accidental over dosages.
Cause, when the only water about is the colour of dirt, the cows, pigs, roos and other animals have been stirring it up, urinating and defecating in it, filtering and or tablets is a waste of time. Boil it.
I've seen people drinking straight from questionable streams without purifying. I think it is unwise. But it's up to them. For me, travelling solo in remote areas, being sick from bad water could turn a lovely journey into an unpleasant struggle. Depending how sick I get, it could turn life threatening and require me to be rescued. The effort to filter then disinfect outweighs the consequences of not doing it. I'm not going to risk it.

